4k^2+8k-73=3

Solution for 4k^2+8k-73=3 equation:

Simplifying
4k2 + 8k + -73 = 3

Reorder the terms:
-73 + 8k + 4k2 = 3

Solving
-73 + 8k + 4k2 = 3

Solving for variable 'k'.

Reorder the terms:
-73 + -3 + 8k + 4k2 = 3 + -3

Combine like terms: -73 + -3 = -76
-76 + 8k + 4k2 = 3 + -3

Combine like terms: 3 + -3 = 0
-76 + 8k + 4k2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-19 + 2k + k2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-19 + 2k + k2)' equal to zero and attempt to solve:

Simplifying
-19 + 2k + k2 = 0

Solving
-19 + 2k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + 2k + 19 + k2 = 0 + 19

Reorder the terms:
-19 + 19 + 2k + k2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 2k + k2 = 0 + 19
2k + k2 = 0 + 19

Combine like terms: 0 + 19 = 19
2k + k2 = 19

The k term is 2k.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2k + 1 + k2 = 19 + 1

Reorder the terms:
1 + 2k + k2 = 19 + 1

Combine like terms: 19 + 1 = 20
1 + 2k + k2 = 20

Factor a perfect square on the left side:
(k + 1)(k + 1) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(k + 1) equal to 4.472135955 and -4.472135955.

Subproblem 1
k + 1 = 4.472135955

Simplifying
k + 1 = 4.472135955

Reorder the terms:
1 + k = 4.472135955

Solving
1 + k = 4.472135955

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + k = 4.472135955 + -1

Combine like terms: 1 + -1 = 0
0 + k = 4.472135955 + -1
k = 4.472135955 + -1

Combine like terms: 4.472135955 + -1 = 3.472135955
k = 3.472135955

Simplifying
k = 3.472135955

Subproblem 2
k + 1 = -4.472135955

Simplifying
k + 1 = -4.472135955

Reorder the terms:
1 + k = -4.472135955

Solving
1 + k = -4.472135955

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + k = -4.472135955 + -1

Combine like terms: 1 + -1 = 0
0 + k = -4.472135955 + -1
k = -4.472135955 + -1

Combine like terms: -4.472135955 + -1 = -5.472135955
k = -5.472135955

Simplifying
k = -5.472135955

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {3.472135955, -5.472135955}
Solution
k = {3.472135955, -5.472135955}